Fill in the blanks to complete the equation of the trend line that contains the points (1,77) and (3,40).

Question

Elapsed time (T) Distance from finish line (D)
1 77
2 55
3 40
4 17

Answer 1

Elapsed time (T) Distance from finish line (D)
1 77
2 55
3 40
4 17

The equation of the trend line can be represented as:

Distance = slope * Elapsed time + y-intercept

To find the slope, we can use the formula:

slope = (Δy) / (Δx)

Where Δy is the change in the distance and Δx is the change in the elapsed time.

Δy = 17 - 77 = -60
Δx = 4 - 1 = 3

slope = -60 / 3 = -20

We can substitute the value of slope (-20) and one of the given points (1, 77) into the equation to calculate the y-intercept.

77 = -20 * 1 + y-intercept
77 = -20 + y-intercept
y-intercept = 77 + 20
y-intercept = 97

Therefore, the completed equation of the trend line is:

Distance = -20 * Elapsed time + 97